When [tex]16x^3 - 12x^2 + 4x[/tex] is divided by [tex]4x[/tex], the quotient is:

When 16 x 3 − 12 x 2 + 4 x is divided by (4x), the quotient is 4 x 2 − 3 x + 1 .[/tex]

To find the quotient when 16x^3 - 12x^2 + 4x\) is divided by (4x), we use polynomial division. Divide the leading term of the numerator, \[tex](16x^3\ by the divisor, (4x), to get 4 x 2 ,[/tex] which is the leading term of the quotient. Then, multiply the divisor (4x) by 4x^2 - 3x + 1\) to get \(16x^3 - 12x^2 + 4x\ Subtract this result from the original polynomial to ensure the remainder is zero.
The division process involves subtracting the product of the divisor and the quotient from the original polynomial. In this case, 16x^3 - 12x^2 + 4x - (4x^2 - 3x + 1) = 0\ confirming that 4x^2 - 3x + 1\) is the correct quotient. Therefore, when [tex]\(16x^3 - 12x^2 + 4x\) is divided by \(4x\), the quotient is \(4x^2 - 3x + 1\
Understanding polynomial division is crucial in algebra, particularly when dealing with higher-degree polynomials. The quotient represents the result of the division, and ensuring the remainder is zero verifies the accuracy of the quotient. In this case, the quotient 4x^2 - 3x + 1\) correctly captures the division of \(16x^3 - 12x^2 + 4x\) by \(4x\

Answered by tokoyoknows | 2024-06-18

The quotient when 16 x 3 − 12 x 2 + 4 x is divided by 4 x is 4 x 2 − 3 x + 1 . This is found using polynomial long division. The process checks the accuracy by ensuring the remainder is zero.
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Answered by tokoyoknows | 2024-10-10